What is the limit as x approaches 3 of (x-3)csc(pix) ?

The limit as x approaches 3 of (x-3)csc(pix) is -1/pi

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limit as x approaches 3 of (x-3)csc(pix)

x \to 3 lim ((x - 3) csc (π x))

- \frac{1}{π}

Decimal

- 0.31830 \dots

Solution steps

x \to 3 lim ((x - 3) csc (π x))

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

x \to 3 - lim ((x - 3) csc (π x)) = - \frac{1}{π}

x \to 3 + lim ((x - 3) csc (π x)) = - \frac{1}{π}

= - \frac{1}{π}

x \to - \frac{1}{2} lim (x)

n \to \infty lim ((\frac{n + 1}{n + 2})^{n + 2})

x \to - \infty lim (x - x^{2})

x \to 20 lim (x^{2} + 1)

h \to 0 lim (\frac{1}{h + 1})

What is the limit as x approaches 3 of (x-3)csc(pix) ?
The limit as x approaches 3 of (x-3)csc(pix) is -1/pi